Posting for reference and also to look at perhaps getting Omniscope to be more efficient and able to handle the sources directly. Currently most of these resources take a bit of time to load up in the Omniscope map view due to their size and granularity.
ArcGIS: http://forums.visokio.com/discussion/2637 The ArcGIS API will have some of those boundaries that can be accessed with a free public account you just have to sign up for a trial to get some login information for the software. Also every year ArcGIS provides a couple of online MOOCs where you can get some extra help regarding their products.
To get these into Omniscope you need to 1) Convert OSGB shapefiles into WGS version shapefile/kml - import/load up your shapefile into your GIS package of choice and set the current projection to OSGB, then go into the save as/export options and change the resulting output into WGS projection. I would suggest you save as .kmls as they appear to be the leanest option.
2) Generalise/clip the shapefiles to reduce the load time (also reduces accuracy), load up the shapefile in you GIS package, find the generalisation options either inbuilt in some packages i.e. model builder with spatial analyst for ArcGIS or install plugins for GrassGIS/QGIS like generalizer/simplify. Just google how to use each package for tutorials/videos on GIS users who use them.
Other options would be to use programming/scripting like in R or Python to do the same generalisation with their own specific libraries but I find the GIS packages will be far quicker to process them.
Unfortunately there is only so much you can generalise/simplify, every iteration of this will erode the quality and accuracy of your boundaries so you have to make the call on how much you want it to simplify to and just do it by trial and error. Including a shapefile in Omniscope significantly bumps up the size of the total Omniscope iok file and affects the loading time and the amount of RAM your machine will also determine what loads.